WASHINGTON — Senator Claire McCaskill, Democrat of Missouri, was the first to take to the Senate floor to publicly pose a question gnawing at an increasing number of lawmakers and ordinary citizens alike as the deadline for a government shutdown neared: Has Congress gone completely crazy?

“It’s very hard from a distance to figure out who has lost their minds,” said Ms. McCaskill immediately after the Senate on Monday rejected a Republican plan to not finance the government unless Democrats agreed to delay the new health law. “One party, the other party, all of us, the president.”

Senator Harry Reid, the Nevada Democrat and majority leader, had his own colorful, if somewhat skewed, metaphor about why much of the government was about to grind to halt in a take-no-political-prisoners fight over what is essentially a simple six-week funding bill, attributing it to the emergence of a “banana Republican mind-set.”

Mr. Reid’s language was evocative, and the implication was serious. With Democrats controlling the White House and Senate and with millions of dollars spent getting the health care law to the starting line, what gives House Republicans the idea that they can triumph in their push to repeal, or at least delay, the Affordable Care Act when so many veteran voices in their party see it as an unwinnable fight?

“Because we’re right, simply because we’re right,” said Representative Steve King, Republican of Iowa, one of the most conservative of House lawmakers. “We can recover from a political squabble, but we can never recover from Obamacare.”

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Pelosi on 'Tea Party Shutdown'

Just before midnight on Monday, Representative Nancy Pelosi, the House Democratic leader, called House Republicans "anti-government ideologues" who intended to shut down the government.

Representative Raúl Labrador, Republican of Idaho and one of the original proponents of the so-called Defund Obamacare movement, was similarly sanguine. “We can always win,” he said Monday afternoon, as he jogged up the stairs to a closed-door conference meeting, where House Republicans gathered to plot their next move.

Representative Pete Sessions, Republican of Texas and chairman of the House Rules Committee, hinted that Republicans were unlikely to give up without at least another round since they see their campaign against the health care law as something of a higher quest. And many, if not most, people they talk to — colleagues, friendly constituents, activists, members of advocacy groups — reinforce that opinion, bolstering their belief that they are on the right side not just ideologically, but morally as well.

“This isn’t the end of the road, guys,” Mr. Sessions said with a grin. “This is halftime.”

The distance between the House and the White House has never seemed greater.

While some House Republicans postulate that President Obama would secretly welcome a postponement of the law to avoid embarrassing bureaucratic problems, he has repeatedly made it clear that he would veto any bill that delays his signature health care law from taking full effect. But he would almost certainly never have to use his veto pen since Mr. Reid, who is incensed at Congressional conservatives, has also made clear that the Senate is unlikely to pass any spending bill that includes items from a Republican wish list, like delaying the health care law for individuals by one year.

As the House and Senate exchanged legislative volleys, the president accused his Republican opponents of an outrageous effort at extortion and reminded them that even if the government does shut down, his health care law will proceed largely unaltered.

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Senator Harry Reid has made clear that the Senate is unlikely to pass any spending bill that includes items from a Republican wish list.Credit
Doug Mills/The New York Times

“An important part of the Affordable Care Act takes effect tomorrow,” Mr. Obama said, referring to the open enrollment process that begins Tuesday. “That funding is already in place. You can’t shut it down.”

Yet House Republicans remain undaunted — and some even said publicly that winning is beside the point.

“What was I elected for? To try to change the law on behalf of my constituents, to stand on my core principles and do my best to represent them ethically, honestly, based on the core principles we share,” said Representative John Culberson, Republican of Texas. “This is a matter of core principle.”

Representative Steve Pearce, Republican of New Mexico, described the task facing his colleagues as perhaps quixotic, but ideologically critical. “At times, you must act on principle and not ask what cost, what are the chances of success,” he said.

Historically, stopgap measures to finance the government were routinely approved with bipartisan support and considered on their own merits as “disputes about money,” as Senator Barbara A. Mikulski, Democrat of Maryland, reminded her colleagues on the Senate floor on Monday. “They were not about political, ideological viewpoints over past legislation,” she said.

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Workers passed the Capitol on Monday.Credit
Doug Mills/The New York Times

After being criticized by the Senate once again, House Republicans emerged Monday afternoon from their closed-door meeting with their latest distinctly political offering to the Senate, a bill that would link further government spending to a one-year delay of the new insurance requirement for individuals, as well as a proposal to force members of Congress, their staff, and White House staff, to buy their health coverage on the new exchanges without any government subsidies to offset the cost.

Senate Democrats immediately decried the plan as unacceptable, and even a portion of House Republicans expressed concern, angry that their leadership’s proposal did not go far enough. Representative Michele Bachmann, Republican of Minnesota, said the only bill she could support would be one that included “a full repeal for a year, which would be defund and delay.”

As the government inched closer to a shutdown, some House Republicans began expressing frustration at what they viewed as magical thinking from some of their colleagues.

“It’s just leading us into a dead end,” said Representative Peter T. King, Republican of New York, referring to his conference’s latest offering. “The Democrats are going to reject it, and the government’s going to shut down.”

Representative Devin Nunes, Republican of California, likened the hard-line, conservative members of his conference to “lemmings with suicide vests.”

“It’s kind of an insult to lemmings to call them lemmings, so they’d have to be more than just a lemming, because jumping to your death is not enough,” he said.

A version of this article appears in print on October 1, 2013, on Page A1 of the New York edition with the headline: Conservatives With a Cause: ‘We’re Right’. Order Reprints|Today's Paper|Subscribe